Yeah :) Additionally, are there any tips you can give for identifying those type of formations/patterns? Or have you simply developed an instinct through experience?

I'd be lying if I said I could have easily spotted the quadratic equation when first studying logs. When you see a2x in an equation, I always keep in mind that it's equivalent to (ax)2 and thus might involve quadratics.

These are also some of the kinds of problems they use to try and throw you off, because students instinctively think: Well, there are exponentials so I need to use logs, but as you now know, that's not the case.